Complex 3D beating heart models are now available, but their complexity makes calibration and validation very difficult tasks. We thus propose a systematic approach of deriving simplified reduced-dimen\-sional models, in ''0D'' --~typically, to represent a cardiac cavity, or several coupled cavities --~and in ''1D'' --~to model elongated structures such as muscle samples or myocytes. We apply this approach with an earlier-proposed 3D cardiac model designed to capture length-dependence effects in contraction, which we here complement by an additional modeling component devised to represent length-dependent relaxation. We then pre\-sent experimental data produced with rat papillary muscles samples when varying preload and afterload conditions, and we achieve some detailed validations of the 1D model with these data, including for the length-dependence effects that are accurately captured. Finally, when running simulations of the 0D model pre-calibrated with the 1D model parameters, we obtain pressure-volume indicators of the left ventricle in good agreement with some important features of cardiac physiology, including the so-called Frank-Starling mechanism, the End-Systolic Pres\-sure-Volume Relationship (ESPVR), as well as varying elastance properties. This integrated multi-dimensional modeling approach thus sheds new light on the relations between the phenomena observed at different scales and at the local vs. organ levels.